JP7144676B2 - Information processing device, quality-related expression generation method, and quality-related expression generation program - Google Patents

Description

The present invention relates to an information processing device, a quality-related formula generating method, and a quality-related formula generating program.

At a product manufacturing site, workers improve the quality of products, such as reducing the defect rate and reducing the variation in quality. For quality improvement, it is important to analyze the data obtained in the manufacturing process and accurately grasp the phenomena occurring in the manufacturing process.

As a data analysis technique, for example, there is a manufacturing process analysis method that can obtain a cause-and-effect model that does not depend on analysts in order to obtain a highly accurate and general-purpose model by multiple regression analysis. An operating condition evaluation device is also being considered that evaluates the operating condition of a process by constructing an operating evaluation function using operating factors that greatly affect the quality of the operating condition as input variable data. Furthermore, when the operational factor space is divided in order to analyze the relationship between operational factors and quality, we also considered an operational and quality related analysis device that enables the construction of a highly accurate quality-operation related model with a relatively small number of divisions. It is There is also a data analysis device that allows batches to be linked to each other and can accurately examine the correlation between variables with different sampling periods and between variables across processes. There is also a product quality improvement support system that makes it easy to know which process causes a defect, and which parameter contributes to what degree to the defect, even if the product contains new parts.

JP 2008-084039 A JP 2013-140548 A JP-A-2006-155557 JP 2009-187175 A JP-A-10-040289

However, the conventional techniques do not provide sufficient accuracy in specifying the causes of defects and factors affecting quality. Therefore, it takes time to improve the product quality.
In one aspect, the present invention aims to improve the accuracy of identifying factors affecting quality.

One proposal provides an information processing apparatus having a storage unit and a processing unit described below.
The storage unit stores measurement data indicating temporal changes in measured values obtained by measuring physical quantities during work on each of a plurality of products of the same type, and quality data including quality values indicating the quality of each of the plurality of products. The processing unit generates a plurality of candidate formulas including coefficients whose values are undetermined and representing temporal changes in physical quantities. Next, the processing unit treats each of the generated candidate formulas as evaluation targets, and determines the coefficient values of the coefficients of the candidate formulas to be evaluated for each product based on the measured values. Next, the processing unit calculates a matching coefficient indicating the degree of conformity of the candidate formula to be evaluated to the measured value based on the coefficient value of the candidate formula to be evaluated for each product. Next, the processing unit calculates the correlation coefficient between the coefficient value and the quality value for each product of the candidate formula to be evaluated. Next, the processing unit calculates the score value of the candidate expression to be evaluated based on the matching coefficient and the correlation coefficient of the candidate expression to be evaluated. Then, the processing unit identifies a quality-related formula including coefficients related to the quality of a plurality of products from among the plurality of candidate formulas based on the score values of each of the plurality of candidate formulas.

According to one aspect, it is possible to improve the accuracy of identifying factors affecting quality.

1 illustrates an example of an information processing apparatus according to a first embodiment; FIG. It is a figure which shows the system configuration example of 2nd Embodiment. It is a figure which shows one structural example of the hardware of a computer. FIG. 4 is a block diagram showing an example of the functions of each device for identifying causes of quality influence; It is a figure which shows an example of the data stored in the manufacturing data storage part. It is a figure which shows an example of the data stored in a formula candidate element memory|storage part. It is a figure which shows an example of the data stored in a theoretical model memory|storage part. It is a figure which shows an example of the data stored in a response characteristic data memory|storage part. 7 is a flow chart showing an example of the procedure of quality influence cause identification processing; FIG. 10 is a diagram illustrating an example of generating candidate models based on set elements; FIG. 4 is a diagram showing an example of candidate models generated using GP; It is a figure which shows an example of generation evolution by crossover. It is a figure which shows the example of calculation of a coefficient value. It is a figure which shows the calculation example of a matching coefficient. It is a figure which shows an example of the data stored in the analysis result memory|storage part. FIG. 5 is a diagram showing an example of correlation analysis between coefficient values and final vacuum degrees; FIG. 11 is a diagram showing an example of calculation of score values of candidate models; It is a figure explaining the difference of a score value by the difference of a calculation method. It is a figure which shows an example of the evaluation result management table in which the evaluation result of the candidate model was set. It is a figure which shows an example of a model matching process. FIG. 4 is a diagram showing an example of filtering of a theoretical model; It is a figure which shows an example of a character string replacement process. FIG. 10 is a diagram showing a first calculation example of the Levenshtein distance; FIG. 10 is a diagram showing a second calculation example of the Levenshtein distance; It is a figure which shows an example of a similarity management table. It is a figure which shows an example of the analysis result display screen of a quality related factor. It is a figure explaining the determination accuracy by a score value. FIG. 2 shows a first example of the structure of formulas for products; FIG. 11 shows a second example of the structure of formulas for products; FIG. 11 illustrates a third example of the structure of formulas for products; FIG. 10 is a diagram showing a fourth example of the structure of formulas for products; FIG. 11 is a flow chart showing an example of the procedure of quality influence cause identification processing according to the third embodiment; FIG. It is a figure which shows the calculation example of a structure evaluation value. It is a figure which shows an example of a ranking management table. It is a figure which shows the example of matching with a candidate model and a theoretical model. It is a figure which shows an example of the analysis result display screen of a quality related factor. FIG. 10 is a diagram showing an example of a display screen for analysis results of quality-related factors when there are a plurality of basic structures;

Hereinafter, this embodiment will be described with reference to the drawings. It should be noted that each embodiment can be implemented by combining a plurality of embodiments within a consistent range.
[First embodiment]
First, a first embodiment will be described.

1 is a diagram illustrating an example of an information processing apparatus according to a first embodiment; FIG. In the first embodiment, the information processing apparatus 10 implements the quality relational expression generation method to generate an expression (quality relational expression) representing the relationship between the factors affecting the quality of a plurality of products and the characteristics of the product. to generate For example, the information processing apparatus 10 implements the quality relational expression generation method by executing a quality relational expression generation program in which the procedure of the quality relational expression generation method is described.

The information processing device 10 has a storage unit 11 and a processing unit 12 . The storage unit 11 is, for example, a memory included in the information processing device 10 or a storage device. The processing unit 12 is, for example, a processor or an arithmetic circuit included in the information processing device 10 .

The storage unit 11 has measurement data 11a and quality data 11b. The measurement data 11a is data indicating changes over time in physical quantities measured during work on each of a plurality of products of the same type. The quality data 11b is data including quality values representing the quality of each of a plurality of products. The quality data 11b may be included in the measurement data 11a. For example, the best value of the measured values for each product in the measurement data 11a or the final value over time may be used as the quality value in the quality data 11b.

The processing unit 12 first generates a plurality of candidate formulas including coefficients whose values are undetermined and representing changes in physical quantities over time. For example, the processing unit 12 generates a plurality of candidate formulas by genetic programming. The candidate formula is a model candidate that quantitatively expresses the temporal change of the physical quantity.

Next, the processing unit 12 calculates a score value for each of the generated candidate formulas based on the measurement data 11a and the quality data 11b. The procedure for calculating the score value is as follows.
The processing unit 12 sequentially selects each of the plurality of generated candidate expressions as an evaluation target. Next, the processing unit 12 determines the coefficient values of the coefficients of the candidate formulas to be evaluated for each product based on the measured values. For example, the processing unit 12 uses the method of least squares to determine the coefficient values that most accurately represent the changes in the measured values of the product. The method of least squares is a method of determining coefficients that minimize the sum of squares of residuals.

When the coefficient value for each product is determined, the processing unit 12 calculates a matching coefficient indicating the degree of conformity of the candidate formula to be evaluated to the measured value based on the coefficient value for each product of the candidate formula to be evaluated. For example, the processing unit 12 calculates the residual between the regression formula obtained by setting the coefficient value for each product to the candidate formula to be evaluated and the measured value for each product, and the average of the absolute values of the residuals is used as the matching coefficient. do. In this case, the more the candidate formula fits the measured value, the smaller the value of the matching coefficient.

Next, the processing unit 12 calculates the correlation coefficient between the coefficient value and the quality value for each product of the candidate formula to be evaluated. The absolute value of the correlation coefficient increases as the correlation increases. Therefore, the processing unit 12 obtains a corrected correlation coefficient, which is corrected such that the correlation coefficient decreases as the correlation increases. For example, the processing unit 12 sets "1-absolute value of correlation coefficient" as the modified correlation coefficient.

After calculating the matching coefficient and the correlation coefficient of the candidate expression to be evaluated, the processing unit 12 calculates the score value of the candidate expression to be evaluated based on the matching coefficient and the correlation coefficient. For example, the processing unit 12 sets the product of the matching coefficient and the value corresponding to the correlation coefficient (corrected correlation coefficient) for the candidate expression to be evaluated as the score value of the candidate expression to be evaluated. When the candidate expression to be evaluated includes a plurality of coefficients, the processing unit 12 generates, for example, a value (corrected correlation coefficient) corresponding to the larger absolute value of the correlation coefficients of the coefficients, and a matching coefficient and the score value of the candidate expression to be evaluated.

When the score values of all the generated candidate formulas are obtained, the processing unit 12 selects the quality factor including coefficients related to the quality of the plurality of products from among the plurality of candidate formulas based on the score values of each of the plurality of candidate formulas. Identify the relevance formula. For example, the processing unit 12 identifies the candidate formula with the lowest score value as the quality-related formula. In addition, the processing unit 12 may select a predetermined number of candidate formulas from the lowest score value as the quality-related formula.

Furthermore, the processing unit 12 identifies a similar theoretical formula similar to the quality-related formula from among the multiple theoretical formulas representing the theoretical properties of the multiple products. The processing unit 12 then outputs the physical meaning of the coefficients included in the similarity theoretical formula. When the quality-related expression contains a plurality of coefficients, the processing unit 12 determines the meaning of the coefficient in the similar theoretical model corresponding to the coefficient with the largest absolute value of the correlation coefficient (the smallest value of the modified correlation coefficient). to output For example, the processing unit 12 displays the meaning of the corresponding coefficient on a screen such as a monitor.

In this way, factors affecting product quality can be identified with high accuracy. For example, if the quality relational expression is specified only by the correlation coefficient, then if a candidate formula with a high correlation coefficient happens to exist, that candidate formula will be identified as the quality relational expression. Since such a candidate formula just happens to have a high correlation coefficient, there is no relationship between the coefficients included in this candidate formula and the quality of the product. Therefore, in the information processing apparatus 10, the score value is calculated by combining the correlation coefficient and the matching coefficient. Candidate formulas with small matching coefficient values (suitable for measured values) represent product characteristics. On the other hand, a candidate formula with a high correlation coefficient by chance does not match the measured value because it has a low relationship with the characteristics of the product, resulting in a large matching coefficient. As a result, erroneous identification of a candidate formula with a high correlation coefficient by chance as a quality-related formula is suppressed.

By being able to correctly identify the quality relational expression related to the product quality, it becomes possible to identify the factors affecting the quality with high precision based on the theoretical model similar to the quality relational expression.

Note that the processing unit 12 can also calculate the score value by weighting the matching coefficient and the correlation coefficient (or the corrected correlation coefficient). The weight value is set in the information processing apparatus 10 in advance by the user, for example. For example, if the user knows that the measurements contain a lot of noise, the weight on the matching coefficient is less than the weight on the correlation coefficient. The processing unit 12 multiplies or divides the values corresponding to the matching coefficient and the correlation coefficient of the candidate formula to be evaluated by weights, and sets the sum of the multiplication or division results of the weights as the score value of the candidate formula to be evaluated. . For example, the processing unit 12 multiplies the matching coefficient and the correlation coefficient by weights when calculating the score value so that the score value increases for a candidate formula with a higher degree of relevance to quality. On the other hand, the processing unit 12 divides each of the matching coefficient and the correlation coefficient by the weight when calculating the score value so that the score value is smaller for the candidate expression having a higher degree of relevance to the quality.

The processing unit 12 also determines the order (ranking) of the matching coefficients and the correlation coefficients among the plurality of candidate expressions, and based on the order of the matching coefficients and the correlation coefficients of the candidate expressions to be evaluated, A score value of the candidate expression to be evaluated may be calculated. By calculating the score value based on the ranking, it is possible to prevent one of the values from being greatly reflected in the score value due to the difference in magnitude (order) between the matching coefficient and the correlation coefficient. For example, the absolute value of the correlation coefficient is in the range of 0 or more and 1 or less. On the other hand, the magnitude (order) of the matching coefficient changes depending on what physical quantity is measured. If the score value is calculated based on the ranking, there is no difference in magnitude (order) of values, and matching coefficients and correlation coefficients can be treated equally.

Furthermore, the processing unit 12 can also specify factors affecting quality with higher accuracy using the basic structure of physical quantity calculation formulas based on the characteristics of a plurality of products. For example, the processing unit 12 calculates the structure evaluation value of the candidate formula to be evaluated based on the degree of similarity between the basic structure and the candidate formula to be evaluated. Then, the processing unit 12 calculates the score value of the candidate formula to be evaluated based on the matching coefficient, the correlation coefficient, and the structure evaluation value of the candidate formula to be evaluated. For example, the processing unit 12 sets the product of a value (corrected correlation coefficient) corresponding to the matching coefficient and the correlation coefficient and the structural evaluation value as the score value. The processing unit 12 can also calculate a score value based on the order (ranking) of each of the matching coefficients, correlation coefficients, and structure evaluation values among a plurality of candidate expressions.

By reflecting the structure evaluation value according to the degree of similarity between the basic structure and the candidate formula to be evaluated in the score value, the closer the basic structure is to the candidate formula, the better the score value can be obtained. This makes it possible to specify the appropriate quality-related formula by specifying the basic structure of the formula in advance, even if the formula that expresses the properties of the product is a complex formula that includes multiple functions. becomes. As a result, the factors affecting quality can be specified with high accuracy.

[Second embodiment]
Next, a second embodiment will be described. The second embodiment specifies factors that affect the quality of cooling units in electronic device assembly lines.

FIG. 2 is a diagram illustrating a system configuration example of the second embodiment. A refrigerant filling device 30 for filling the cooling units 1, 2, . . . A computer 100 is connected to the refrigerant charging device 30 . The computer 100 acquires data measured during the process of filling the cooling units 1, 2, . Analyze influencing factors.

For example, the operator connects the refrigerant injection coupler 31 connected by a tube from the refrigerant charging device 30 to the cooling unit 1 . When the operator presses the charging start switch of the refrigerant charging device 30 , the refrigerant charging device 30 evacuates the refrigerant charging space in the connected cooling unit 1 . The refrigerant charging device 30 injects the refrigerant into the refrigerant injection space when the degree of vacuum reaches or exceeds a specified value. The operator removes the coolant injection coupler 31 from the cooling unit 1 when the coolant injection is completed. Refrigerant can be injected into each cooling unit 1, 2, .

Some of the cooling units 1, 2, . In that case, the refrigerant charging device 30 determines that the evacuation has failed. If the vacuuming fails, the operator temporarily stops the cooling unit manufacturing line and vacuums again the cooling unit for which the vacuuming failed.

In this way, the failure of the evacuation causes the production line to stop, and deteriorates the production efficiency. Therefore, in the second embodiment, the computer 100 is used to identify the factors that affect the quality of the evacuation.

FIG. 3 is a diagram showing a configuration example of computer hardware. A computer 100 is entirely controlled by a processor 101 . A memory 102 and a plurality of peripheral devices are connected to the processor 101 via a bus 109 . Processor 101 may be a multiprocessor. The processor 101 is, for example, a CPU (Central Processing Unit), MPU (Micro Processing Unit), or DSP (Digital Signal Processor). At least part of the functions realized by the processor 101 executing the program may be realized by an electronic circuit such as an ASIC (Application Specific Integrated Circuit) or a PLD (Programmable Logic Device).

Memory 102 is used as the main storage device of computer 100 . The memory 102 temporarily stores at least part of an OS (Operating System) program and application programs to be executed by the processor 101 . In addition, the memory 102 stores various data used for processing by the processor 101 . As the memory 102, for example, a volatile semiconductor memory device such as a RAM (Random Access Memory) is used.

Peripheral devices connected to the bus 109 include the storage device 103 , graphic processing device 104 , input interface 105 , optical drive device 106 , device connection interface 107 and network interface 108 .

The storage device 103 electrically or magnetically writes data to and reads data from a built-in recording medium. The storage device 103 is used as an auxiliary storage device for the computer. The storage device 103 stores an OS program, application programs, and various data. As the storage device 103, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive) can be used.

A monitor 21 is connected to the graphics processing unit 104 . The graphics processing unit 104 displays an image on the screen of the monitor 21 according to instructions from the processor 101 . Examples of the monitor 21 include a display device using an organic EL (Electro Luminescence), a liquid crystal display device, and the like.

A keyboard 22 and a mouse 23 are connected to the input interface 105 . The input interface 105 transmits signals sent from the keyboard 22 and mouse 23 to the processor 101 . Note that the mouse 23 is an example of a pointing device, and other pointing devices can also be used. Other pointing devices include touch panels, tablets, touchpads, trackballs, and the like.

The optical drive device 106 reads data recorded on the optical disc 24 using laser light or the like. The optical disc 24 is a portable recording medium on which data is recorded so as to be readable by light reflection. The optical disc 24 includes DVD (Digital Versatile Disc), DVD-RAM, CD-ROM (Compact Disc Read Only Memory), CD-R (Recordable)/RW (ReWritable), and the like.

The device connection interface 107 is a communication interface for connecting peripheral devices to the computer 100 . For example, the device connection interface 107 can be connected to the memory device 25 and the memory reader/writer 26 . The memory device 25 is a recording medium equipped with a communication function with the device connection interface 107 . The memory reader/writer 26 is a device that writes data to the memory card 27 or reads data from the memory card 27 . The memory card 27 is a card-type recording medium.

Network interface 108 is connected to network 20 . Network interface 108 transmits and receives data to and from other computers or communication devices via network 20 .

The computer 100 can implement the processing functions of the second embodiment with the hardware configuration described above. The apparatus shown in the first embodiment can also be realized by hardware similar to the computer 100 shown in FIG.

The computer 100 implements the processing functions of the second embodiment by executing a program recorded in a computer-readable recording medium, for example. A program describing the processing content to be executed by the computer 100 can be recorded in various recording media. For example, a program to be executed by the computer 100 can be stored in the storage device 103 . The processor 101 loads at least part of the program in the storage device 103 into the memory 102 and executes the program. The program to be executed by the computer 100 can also be recorded in a portable recording medium such as the optical disk 24, memory device 25, memory card 27, or the like. A program stored in a portable recording medium can be executed after being installed in the storage device 103 under the control of the processor 101, for example. Alternatively, the processor 101 can read and execute the program directly from the portable recording medium.

The computer 100 having such hardware analyzes the manufacturing data collected by the refrigerant charging device 30, and identifies factors that may cause the occurrence of defective products. Note that the information processing apparatus 10 shown in the first embodiment can also be realized by hardware similar to the computer 100 .

FIG. 4 is a block diagram showing an example of the functions of each device for identifying the cause of quality influence. The refrigerant charging device 30 has a manufacturing data storage section 32 and a control section 33 . The manufacturing data storage unit 32 stores data collected during the manufacturing process of the cooling units 1, 2, . The control unit 33 controls the evacuation of the cooling units 1, 2, . . . and refrigerant injection. In addition, the control unit 33 periodically measures the degree of vacuum in the refrigerant injection space during evacuation, and stores the value of the measured degree of vacuum in the manufacturing data storage unit 32 . Furthermore, in response to a data acquisition request from computer 100 , control unit 33 transmits designated data in manufacturing data storage unit 32 to computer 100 .

The computer 100 includes a mathematical formula candidate element storage unit 110, a theoretical model storage unit 120, a response characteristic data acquisition unit 130, a response characteristic data storage unit 140, a candidate model construction unit 150, a data analysis unit 160, an analysis result storage unit 170, and a model It has an evaluation unit 180 .

The mathematical formula candidate element storage unit 110 stores elements such as operators used to construct a mathematical formula representing time-series changes in the degree of vacuum. The theoretical model storage unit 120 stores, as theoretical models, calculation formulas representing physical phenomena that occur in manufacturing processes such as evacuation of the cooling units 1, 2, . . . . A theoretical model is an example of a theoretical formula in the first embodiment.

The response characteristic data acquisition unit 130 acquires response characteristic data representing time-series changes in physical quantities obtained by observing the product when the product is operated during the manufacturing process. For example, the response characteristic data acquiring unit 130 acquires, from the refrigerant charging device 30, data indicating time-series changes in the degree of vacuum when the cooling units 1, 2, . . . are vacuumed, as response characteristic data. The response characteristic data acquisition section 130 stores the acquired response characteristic data in the response characteristic data storage section 140 . The response characteristic data storage unit 140 stores response characteristic data.

The candidate model construction unit 150 combines the elements stored in the mathematical formula candidate element storage unit 110 or the elements input by the user to create a calculation formula representing the time-series change in the degree of vacuum represented by the response characteristic data. Construct a candidate model that is a candidate. A candidate model is an example of the candidate formula shown in the first embodiment. For example, the candidate model construction unit 150 repeatedly constructs candidate models using a genetic algorithm (GA). When using GA to construct a candidate model, the candidate model constructing unit 150 can efficiently construct a complicated calculation formula by using genetic programming (GP).

The data analysis unit 160 performs data analysis based on the constructed candidate models for each of the cooling units 1, 2, . For example, the data analysis unit 160 compares the constructed candidate model with the response characteristic data of cooling units 1, 2, . 2, . . . are calculated for each. The data analysis unit 160 also calculates a matching coefficient indicating the degree of matching between the candidate model whose coefficient value has been determined and the response characteristic data. The data analysis unit 160 stores data analysis results in the analysis result storage unit 170 . The analysis result storage unit 170 stores analysis results for each candidate model.

The model evaluation unit 180 calculates a score value indicating the extent to which the physical quantities corresponding to the coefficients included in the candidate model affect product quality (final degree of vacuum after evacuation). For example, the model evaluation unit 180 calculates the score value based on the average matching coefficient value for each of the cooling units 1, 2, . . . and the coefficient values included in the candidate models. When the candidate model construction unit 150 constructs candidate models by GA or GP, the model evaluation unit 180 transmits candidate models with excellent score values among the evaluated candidate models to the candidate model construction unit 150 . In the example below, the score value is as good as the value is small. As a result, the candidate model construction unit 150 can construct an appropriate candidate model according to the GA or GP algorithm, such as constructing the next generation candidate model based on the candidate model with the excellent score value. Furthermore, the model evaluation unit 180 determines the physical meaning of the coefficients of the candidate models whose score values are less than the threshold based on the theoretical model. Then, the model evaluation unit 180 displays on the monitor 21 the physical meaning of the coefficient of the candidate model whose score value is less than the threshold value as a factor affecting quality.

The lines connecting the elements shown in FIG. 4 indicate part of the communication paths, and communication paths other than the illustrated communication paths can be set. Also, the function of each element shown in FIG. 4 can be realized by causing the computer 100 to execute a program module corresponding to the element, for example.

Next, with reference to FIGS. 5 to 8, the data used in the process of identifying the cause of quality influence will be described in detail. Of the data used for the quality impact cause identification process, the data stored in the manufacturing data storage unit 32, the formula candidate element storage unit 110, and the theoretical model storage unit 120 are stored before the quality impact cause identification process is executed. be prepared.

FIG. 5 is a diagram illustrating an example of data stored in a manufacturing data storage unit; The manufacturing data storage unit 32 stores, for example, a manufacturing data management table 32a. Quality data and manufacturing data are set in the manufacturing data management table 32a in association with the unit numbers of the cooling units 1, 2, .

The quality data is data indicating criteria for quality of the corresponding cooling unit. For example, the final degree of vacuum is set in the manufacturing data management table 32a as quality data. The degree of vacuum is represented by the atmospheric pressure of the space to be evacuated, and the smaller the value, the higher the degree of vacuum.

In the manufacturing data, the determination result of quality and the degree of vacuum for each elapsed time of vacuuming are set. As a judgment result, if the final degree of vacuum satisfies the specified value (the value of the final degree of vacuum is less than the threshold value), the value "OK" indicating good quality is set, and the final degree of vacuum does not satisfy the specified value ( If the value of the final degree of vacuum is equal to or greater than the threshold value), a value “NG” indicating quality failure is set.

FIG. 6 is a diagram depicting an example of data stored in a formula candidate element storage unit; The mathematical formula candidate element storage unit 110 stores, for example, mathematical formula candidate element lists 111, 112, . . . for each technical field category. Each of the formula candidate element lists 111, 112, . Formula candidate elements include operators, functions, and variables. The operators are, for example, four arithmetic operators. The functions are, for example, trigonometric functions, exponential functions, logarithmic functions. Variables include real numbers and coefficients in addition to variables such as x and y.

By previously listing the functions and the like used in the relevant field for each category in this manner, it is possible to efficiently create an appropriate candidate model. Also, theoretical calculation formulas for physical quantities for each category are registered in advance in the theoretical model storage unit 120 .

FIG. 7 is a diagram depicting an example of data stored in a theoretical model storage unit; The theoretical model storage unit 120 stores, for example, a theoretical model management table 121 . Each record of the theoretical model management table 121 is set with a category, a theoretical model, the meaning of the theoretical model, and the meaning of the coefficient. A category is a technical field to which the corresponding theoretical model applies. A theoretical model is a calculation formula for calculating physical quantities in a corresponding category. The meaning of the theoretical model is the meaning of the physical quantity calculated by the theoretical model. The meaning of the coefficients is the physical meaning of the coefficients contained in the theoretical model. For example, the theoretical model "P(x)=a/x" whose category is "evacuation" is a formula for calculating the evacuation speed, and the coefficient "a" is the evacuation resistance.

After the data shown in FIGS. 5 to 7 are prepared, the response characteristic data acquisition unit 130 acquires manufacturing data from the manufacturing data storage unit 32 as preprocessing for specifying the cause of quality influence. Then, the response characteristic data acquisition unit 130 generates response characteristic data for each of the cooling units 1, 2, . . . based on the acquired manufacturing data, and stores the response characteristic data in the response characteristic data storage unit 140.

FIG. 8 is a diagram of an example of data stored in a response characteristic data storage unit; The response characteristic data storage unit 140 stores response characteristic data 141, 142, . . . for each of the cooling units 1, 2, . A degree of vacuum is set for each of the response characteristic data 141, 142, . The vacuum degree of the last record (with the longest elapsed time) in the response characteristic data 141, 142, . . . is the final vacuum degree of the corresponding cooling unit.

After the response characteristic data 141, 142, . The quality influence cause identifying process will be described in detail below.

FIG. 9 is a flow chart showing an example of the procedure of quality influence cause identification processing. The processing shown in FIG. 9 will be described below along with the step numbers.
[Step S101] The candidate model constructing unit 150 receives input specifying elements (operators, etc.) to be used in constructing candidate models. For example, the user provides inputs specifying what the variables of the candidate model should be, what operators to use, and what functions to use. The user can also specify one of the mathematical expression candidate element lists in the mathematical expression candidate element storage unit 110 instead of inputting the designation of individual elements. When a mathematical expression candidate element list is specified, the candidate model construction unit 150 uses the operators, functions, and variables indicated in the designated mathematical expression candidate element list as elements to be used for constructing the candidate model.

The user can also enter conditions for terminating candidate model building. For example, the user inputs a score value threshold as an end condition. When a score value threshold is input, the candidate model construction unit 150 stores the input threshold as an end condition. Note that, if the threshold value as the termination condition is not input, the candidate model construction unit 150 uses, for example, a preset threshold value as the termination condition.

[Step S102] The candidate model construction unit 150 constructs a candidate model by combining mathematical expression candidate elements by GP. For example, when constructing a first-generation GP candidate model, the candidate model constructing unit 150 constructs a predetermined number (eg, 10) of candidate models by randomly combining formula candidate elements. Further, when constructing candidate models of the second and subsequent generations of the GP, the candidate model constructing unit 150 selects two candidate models with better score values (for example, lower values) from the candidate models that have already been constructed. . Then, the candidate model constructing unit 150 performs operations such as crossover using the selected candidate model as a parent to construct the next generation candidate model.

[Step S103] The data analysis unit 160 calculates values of coefficients included in the constructed candidate model for each of the response characteristic data 141, 142, . For example, the data analysis unit 160 calculates coefficient values of candidate models that fit the response characteristic data by regression analysis. As a result, the calculation formula (regression formula) of the candidate model is determined.

[Step S104] The data analysis unit 160 calculates a matching coefficient for each cooling unit for the constructed candidate model. For example, the smaller the residual between the response characteristic data of the cooling unit and the curve of the candidate model for which the coefficient is set, the smaller the matching coefficient.

[Step S105] The data analysis unit 160 performs correlation analysis between each coefficient in the candidate model and the product quality (final degree of vacuum). Correlation analysis calculates a correlation coefficient for each coefficient of each constructed candidate model. Correlation coefficients are real numbers ranging from -1 to +1. The larger the absolute value of the correlation coefficient, the higher the degree of correlation between the coefficient and the final degree of vacuum. The data analysis unit 160 calculates, for example, "1-absolute value of correlation coefficient" and uses the calculation result as a corrected correlation coefficient. As a result, a modified correlation coefficient whose value decreases as the degree of correlation increases is obtained.

[Step S106] The model evaluation unit 180 calculates the score value of the candidate model based on the corrected correlation coefficient for each coefficient in the candidate model and the matching coefficient indicating the difference between the candidate model and the response characteristic data. .

[Step S107] The model evaluation unit 180 determines whether or not the conditions for terminating construction of the candidate model are satisfied. For example, the model evaluation unit 180 determines that the termination condition is satisfied when there is at least one candidate model whose score value is less than the threshold. If the termination condition is satisfied, the model evaluation unit 180 advances the process to step S108. If the termination condition is not satisfied, the model evaluation unit 180 advances the process to step S102. If the termination condition is not satisfied, the model evaluation unit 180 transmits, for example, two candidate models with the highest score values among the candidate models of the latest generation to the candidate model construction unit 150 .

[Step S108] The model evaluation unit 180 compares a predetermined number of candidate models with the smallest score values with the theoretical model. The model evaluation unit 180 calculates, for example, the structural similarity between the candidate model and the theoretical model. Then, the model evaluation unit 180 determines the meaning of the coefficients of the candidate model based on the meaning of the coefficients of the theoretical model similar to the candidate model.

[Step S109] The model evaluation unit 180 outputs the result of identifying the quality influence cause. For example, the model evaluation unit 180 displays on the monitor 21 the meanings of the coefficients of a predetermined number of candidate models in ascending order of score value as factors affecting product quality.

The process of identifying the cause of quality influence is performed in such a procedure. The processing for identifying the cause of quality influence will be specifically described below.
FIG. 10 is a diagram illustrating an example of generating candidate models based on set elements. For example, the candidate model construction unit 150 acquires the element group 41 by inputting the element designation. The element group 41 includes a variable "t", an operator, and a function as elements that configure the candidate model. Next, the candidate model construction unit 150 uses GP to generate a calculation formula 42 that combines the constituent elements of the candidate model. For example, a calculation formula 42 such as "1/t" is generated.

The candidate model constructing unit 150 assigns coefficients indicating, for example, gain and offset to the generated calculation formula 42 , and uses the obtained calculation formula as a candidate model 43 . The coefficient representing the gain is, for example, a coefficient indicating a value by which the entire calculation formula generated by the GP is to be multiplied. A coefficient indicating an offset is a coefficient indicating a value to be added to a variable. When the calculation formula obtained by GP is "1/t", the candidate model 43 is "a/(t+b)". In this candidate model 43, "a" is a coefficient indicating gain, and "b" is a coefficient indicating offset.

Although the example of FIG. 10 shows an example of the candidate model 43 with a simple structure, it is possible to generate a candidate model with a complicated structure by using GP.
FIG. 11 is a diagram showing an example of candidate models generated using GP. In the example of FIG. 11, the candidate model 44 of the calculation formula "{sin(a+(x×y)+b)+In(c×(y×y))}+exp(z)" is represented by a tree structure. In the tree-structured candidate model 44, the elements specified as the elements become the nodes of the tree structure.

The candidate model construction unit 150 constructs the next-generation candidate model by, for example, performing operations such as crossover and mutation of a part (subtree) of a plurality of tree structures.
FIG. 12 is a diagram showing an example of generational evolution by crossover. The candidate model constructing unit 150 identifies subtrees 45a and 46a from the candidate models 45 and 46, respectively, with the two current generation candidate models 45 and 46 as parents. The subtrees 45a and 46a are, for example, tree structures below nodes randomly selected from nodes other than the root node. The candidate model constructing unit 150 generates two next-generation candidate models 47 and 48 by replacing the subtrees 45a and 46a specified from the candidate models 45 and 46, respectively. The candidate model 47 has a structure in which the partial tree 45a is deleted from the candidate model 45, and a partial tree 47a having the same structure as the partial tree 46a in the candidate model 46 is connected to the position where the partial tree 45a was. The candidate model 48 has a structure in which the partial tree 46a is deleted from the candidate model 46, and a partial tree 48a having the same structure as the partial tree 45a in the candidate model 45 is connected to the position where the partial tree 46a was.

The candidate model construction unit 150 generates a predetermined number of next-generation candidate models by performing generational evolution by crossover on the candidate models 45 and 46 a plurality of times. For example, if the candidate model construction unit 150 performs generational evolution by crossover five times, ten next-generation candidate models are generated.

The candidate model construction unit 150 can also simplify the generated candidate model. For example, when the candidate model includes an addition or subtraction part such as "a+b" in the candidate model, the candidate model construction unit 150 combines the part into one coefficient. For example, it becomes "a+b→a".

Further, the candidate model construction unit 150 may combine multiple terms in the candidate model. For example, when the candidate model includes a plurality of terms “sin(x)×In(y)+sin(x)×log(z)”, the candidate model construction unit 150 converts this part to “sin(x) { In(y)+log(z)}”.

Furthermore, the candidate model construction unit 150 can also check whether the candidate model has an irrational function. An irrational function is a function whose structure is mathematically impermissible. For example, the candidate model construction unit 150 checks whether there is an irrational function such as dividing by zero, outside the domain, or without variables. The division by zero function is a function of division by "0" (a fraction whose denominator is "0"), such as "sin(x)/0". A function outside the domain is a function with a variable outside the mathematical definition, such as "log(-x): x>0" (a logarithm can be defined when the antilogarithm x is an integer). be. A function without variables is a function that does not contain variables, such as "cos(a)" (where a is a coefficient). A function without variables can be replaced by, for example, one coefficient.

When the candidate models are constructed, the data analysis unit 160 calculates the coefficient values of the candidate models.
FIG. 13 is a diagram illustrating an example of calculation of coefficient values. The data analysis unit 160 creates graphs 51, 52, . Then, the data analysis unit 160, for each of the graphs 51, 52, . Calculate the coefficient values in the candidate model 43 . For example, the data analysis unit 160 calculates coefficient values by the method of least squares. Thereby, a coefficient value for each cooling unit is calculated for one candidate model 43 .

Note that in the example of FIG. 13, the candidate model construction unit 150 calculates coefficient values while ignoring the degree of vacuum during a period when the degree of vacuum hardly changes. After calculating the coefficient values, the candidate model construction unit 150 calculates matching coefficients.

FIG. 14 is a diagram illustrating an example of calculation of matching coefficients. The data analysis unit 160 calculates residuals between points plotted on the graph 51 generated for one cooling unit and the candidate model curve 43a. The residual is the distance in the vacuum degree p direction from the plotted point to the candidate model curve 43a. The data analysis unit 160 uses the average of the absolute values of the residuals for each plotted point as the matching coefficient for the corresponding cooling unit. The data analysis unit 160 calculates such a matching coefficient for each cooling unit 1, 2, .

The candidate model construction unit 150 stores the calculation results of the coefficient values and the matching coefficients in the analysis result storage unit 170 .
15 is a diagram depicting an example of data stored in an analysis result storage unit; FIG. The analysis result storage unit 170 stores, for example, analysis result management tables 171, 172, . . . for each candidate model.

Records indicating the analysis results based on the response characteristic data 141, 142, . . . of the cooling units 1, 2, . In each record, the final degree of vacuum, the coefficient value of each coefficient included in the candidate model, and the matching coefficient are set in association with the unit numbers of the cooling units 1, 2, . As a result of the analysis by the data analysis unit 160, coefficient values and matching coefficients for each cooling unit 1, 2, . . . are obtained for each of the constructed candidate models. The average of the matching coefficients calculated for each cooling unit 1, 2, . . . for one candidate model is the matching coefficient of that candidate model.

Here, if the candidate model accurately represents product quality, the coefficient values included in the candidate model are considered to have physical meanings that affect physical phenomena related to product quality. In other words, the candidate model is generated by GP regardless of the laws of nature, but if the candidate model accurately represents the good or bad of product quality, the candidate model is a physical model related to product quality. represents a phenomenon. In this case, the structure of the formulas forming the candidate model represents the characteristics of the physical phenomenon, and the coefficients included in the candidate model also represent the characteristics of the physical phenomenon.

Therefore, the model evaluation unit 180 evaluates the degree to which the coefficients included in the candidate models represent the characteristics of physical phenomena that affect product quality, based on the coefficient values and the matching coefficients. For example, the model evaluation unit 180 performs correlation analysis between the coefficient values of the coefficients included in the candidate model and the final degree of vacuum.

FIG. 16 is a diagram showing an example of correlation analysis between coefficient values and final degrees of vacuum. When the candidate model includes a plurality of coefficients, the model evaluation unit 180 performs correlation analysis for each coefficient and calculates a correlation coefficient. In the example of FIG. 16, correlation coefficients are calculated for two coefficients a and b included in the candidate model "a/(t+b)". The correlation coefficient between the coefficient a and the final degree of vacuum is "0.86", and the correlation coefficient between the coefficient b and the final degree of vacuum is "0.25". Since the larger the absolute value of the correlation coefficient, the higher the correlation, the coefficient a has a higher correlation with the final degree of vacuum than the coefficient b.

Based on the calculated correlation coefficient, the model evaluation unit 180 calculates a modified correlation coefficient that becomes a smaller value as the correlation is higher. The corrected correlation coefficient is represented by "corrected correlation coefficient=1-absolute value of correlation coefficient of coefficient". The model evaluation unit 180 then sets the modified correlation coefficients in the evaluation result management table 181 .

The evaluation result management table 181 registers, for example, matching coefficients, corrected correlation coefficients for each coefficient, and score values in association with candidate models. The matching coefficient registered in the evaluation result management table 181 is, for example, an average value of matching coefficients calculated for each cooling unit 1, 2, . Since the score value has not been calculated at the stage shown in FIG. 16, the score value column of the candidate model "a/(t+b)" is blank.

The model evaluation unit 180 stores the evaluation result management table 181 in the memory 102, for example. Then, the model evaluation unit 180 calculates the score value of the candidate model based on the matching coefficient set in the evaluation result management table 181 and the corrected correlation coefficient for each coefficient of the candidate model.

FIG. 17 is a diagram illustrating an example of calculation of score values of candidate models. When one candidate model includes a plurality of coefficients, the model evaluation unit 180 selects the coefficient with the smaller modified correlation coefficient value, and treats the selected coefficient as the quality-related feature. The model evaluator 180 then calculates the product of the modified correlation coefficient of the quality-related feature and the matching coefficient. Then, the model evaluation unit 180 sets the product calculation result in the evaluation result management table 181 as a score value.

As a result, the smaller the value of the modified correlation coefficient of the quality-related feature, the smaller the score value, and the smaller the value of the matching coefficient, the smaller the score value. Even if the score value is the sum of the corrected correlation coefficient of the quality-related feature and the matching coefficient, the score value will be smaller as the value of the corrected correlation coefficient of the quality-related feature is smaller. The smaller the value, the smaller the value. However, in order to find a coefficient that achieves both a small matching coefficient and a small corrected correlation coefficient, it is better to use the product of the corrected correlation coefficient of the quality-related feature and the matching coefficient as the score value.

FIG. 18 is a diagram for explaining differences in score values due to differences in calculation methods. FIG. 18 shows an evaluation result coordinate system 60 representing evaluation results. The horizontal axis of the evaluation result coordinate system 60 is the matching coefficient, and the vertical axis is the corrected correlation coefficient. The evaluation result is located somewhere in the evaluation result area 61 in the first quadrant. When calculating the score value, when the evaluation result is at the position (target position 64) where the matching coefficient is the minimum "0" and the correction correlation coefficient is the minimum "0", the score value is the minimum (best). It is appropriate to use a simple calculation formula.

FIG. 18 shows two evaluation results 62 and 63 . One evaluation result 62 has a matching coefficient of "99.9" and a corrected correlation coefficient of "0.1". The other evaluation result 63 has a matching coefficient of "99.1" and a corrected correlation coefficient of "0.9".

As a method of calculating the score value, if the sum of the two coefficients is taken, both results will be a score value of "100" and there will be no difference. However, as can be seen by arranging the evaluation results 62 and 63 on the evaluation result coordinate system 60 , the evaluation result 62 is closer to the target position 64 . By adopting the product of two coefficients as a score value calculation method, the score value of the evaluation result 62 is smaller than that of the evaluation result 63 (becomes an excellent score value). Therefore, the model evaluation unit 180 uses the product of the matching coefficient and the corrected correlation coefficient as the score value.

The model evaluation unit 180 calculates a corrected correlation coefficient and a score value for each constructed candidate model each time a candidate model is iteratively constructed by the GP. The model evaluation unit 180 then sets the calculation result in the evaluation result management table 181 . This process is repeated until the conditions for terminating candidate model construction are met.

FIG. 19 is a diagram illustrating an example of an evaluation result management table in which evaluation results of candidate models are set. A score value is calculated for each candidate model, as shown in FIG. For a candidate model containing multiple coefficients, the coefficient with the lowest corrected correlation coefficient value among the coefficients of the candidate model is the quality-related feature used to calculate the score value. Of the candidate models shown in the evaluation result management table 181, the smaller the score value, the higher the relevance of the quality-related features included in the candidate model to the product quality.

Once the candidate model's termination conditions are met, the model evaluator 180 examines the meaning of quality-related features that are highly relevant to product quality by matching the candidate model to the theoretical model.
FIG. 20 is a diagram illustrating an example of model matching processing. For example, it is assumed that the formula of the candidate model 71 with the lowest score value (good evaluation) is "a/(t+b)". It is also assumed that the quality-related feature in this candidate model 71 is the coefficient a.

The model evaluation unit 180 collates the formula of the corresponding candidate model 71 with the formula of each theoretical model registered in the theoretical model management table 121, and extracts a similar theoretical model. In the example of FIG. 20 , the theoretical model “P(x)=a/x” has a high degree of similarity with the candidate model 71 .

In this case, the model evaluation unit 180 sets the meaning “exhaust resistance” of the coefficient “a” corresponding to the quality-related feature in the theoretical model “P(x)=a/x” with a high degree of similarity to the theoretical model management table 121. Extract from Then, the model evaluation section 180 displays on the monitor 21 that the exhaust resistance affects the product quality.

The model matching process will be described in detail below.
In the model matching process, the model evaluation unit 180 first filters the theoretical model. Filtering is a process of excluding theoretical models that are clearly not similar to candidate models from similarity calculation targets.

FIG. 21 is a diagram illustrating an example of theoretical model filtering. In the example of FIG. 21, it is assumed that the formula of the candidate model 72 with the highest evaluation is "a*sin(b*x+c)". At this time, the model evaluation unit 180 first analyzes the configuration of each theoretical model. Then, the theoretical model configuration information 73 is generated. For example, the model evaluation unit 180 analyzes the type of function, the number of variables, and the degree of each theoretical model, and sets the determination result in the theoretical model configuration information 73 . Similarly, the model evaluation unit 180 analyzes the type of function, the number of variables, and the degree of the candidate model 72 as well.

Then, the model evaluation unit 180 deletes from the theoretical model configuration information 73 the candidate model 72 and the theoretical model that does not match any one of the type of function, the number of variables, and the order. Note that the model evaluation unit 180 may regard functions such as sin and cos, which have only a phase difference, as the same function. In the example of FIG. 21, the function of candidate model 72 is "sin". On the other hand, the theoretical model "a/x" shown in the theoretical model configuration information 73 does not contain the function "sin". Therefore, the model evaluation unit 180 deletes the theoretical model “a/x” from the theoretical model configuration information 73 and excludes it from the similarity calculation target. Also, the function of the theoretical model “aexp(−bx)” (the multiplication sign is omitted) is “exp”, which is different from the function “sin” of the candidate model 72 . Therefore, the model evaluation unit 180 deletes the theoretical model “aexp(-bx)” from the theoretical model configuration information 73 and excludes it from similarity calculation targets.

Such filtering processing narrows down the theoretical models for which the similarity is to be calculated. Next, the model evaluation unit 180 replaces the character strings between the candidate model and the theoretical model.
FIG. 22 is a diagram illustrating an example of character string replacement processing. For example, a replacement rule 74 is defined in advance in the model evaluation unit 180 . In the replacement rule 74, a character string to be replaced is set in association with the element to be replaced. In the example of FIG. 22, the replacement rule 74 is defined such that the replacement source element is replaced with one character.

The model evaluation unit 180 replaces the character strings for each of the candidate model and the theoretical model according to the replacement rule 74 . For example, the model evaluation unit 180 replaces the function "sin" of the candidate model "asin(bx+a)" (the multiplication sign is omitted) with "f". The model evaluation unit 180 also replaces the coefficients "a, b" of the candidate model "asin(bx+a)" with "a".

Similarly, the model evaluation unit 180 replaces the character strings of the theoretical model according to the replacement rule 74 as well. For example, the variable "t" in the theoretical character string "asin(ωt+θ)" (the multiplication sign is omitted) is replaced with "x".

Next, the model evaluation unit 180 compares the degree of similarity between the character string of the candidate model after replacement and the character string of the theoretical model after replacement by the Levenshtein distance method. The Levenshtein distance can be calculated using, for example, a two-dimensional matrix.

FIG. 23 is a diagram illustrating a first calculation example of the Levenshtein distance. FIG. 23 shows the Levenshtein distance between the candidate model "a×f(a×x+a)" after replacement and the theoretical model "a ² ×f ² (x)×g ² (x)" after replacement. Examples are given. The first row and first column of the Levenshtein distance calculation matrix 75a correspond to null characters. In each line, the character of the candidate model after replacement is associated in order from the beginning after the blank character. In each column, the character of the theoretical model after replacement is associated in order from the beginning after the empty character. The distance between one character of the candidate model after replacement and one character of the theoretical model after replacement is set in the cells corresponding to those characters.

The distance between an empty character in one character string and the n-th character (n is an integer equal to or greater than 1) in the other character string is n. Other cells are set to the smallest value among the following three numbers.
・ The number of the square above your own square + 1
・ The number in the left square of your own square + 1
・The number in the upper left square of your own square + a (a is “0” if the vertical and horizontal characters of your own square are the same, and “1” if they are different)
The number "8" in the lower right corner of the matrix 75a thus created is the Levenshtein distance (minimum number of edits) between the candidate model after replacement and the theoretical model after replacement.

FIG. 24 is a diagram illustrating a second calculation example of the Levenshtein distance. FIG. 24 shows an example of obtaining the Levenshtein distance between the candidate model “a×f(a×x+a)” after replacement and the theoretical model “a×f(x)” after replacement. The number in the lower right corner of the Levenshtein distance calculation matrix 75b shown in FIG. 24 is "4", and the Levenshtein distance is "4".

The model evaluation unit 180 uses the calculated Levenshtein distance as the degree of similarity. After calculating the similarity of each logical model, the model evaluation unit 180 compares the similarity of each logical model and ranks them in descending order of similarity. Then, the model evaluation unit 180 creates a similarity management table indicating the order of similarity of the theoretical models.

The model evaluation unit 180 calculates the degree of similarity with a theoretical model for each of a predetermined number of candidate models with the highest score value, for example, and creates a degree of similarity management table.
FIG. 25 is a diagram showing an example of a similarity management table. As shown in FIG. 25, similarity management tables 76a, 76b, . . . are created for each candidate model. The similarity management tables 76a, 76b, . The model evaluation unit 180 stores the created similarity management tables 76a, 76b, . . .

The model evaluation unit 180 identifies the coefficient corresponding to the quality-related feature of the theoretical model with high similarity to the candidate model with the low score value (high evaluation), and uses the coefficient to influence the quality of the product. It is a quality-related factor with a high probability. The model evaluation unit 180 displays the analysis results of quality-related factors on the monitor 21 .

FIG. 26 is a diagram showing an example of an analysis result display screen of quality-related factors. The analysis result display screen 77 includes, for example, quality-related factor information 77a. The quality-related factor information 77a indicates quality-related factors obtained from similar theoretical models for each candidate model.

For example, in the quality-related factor information 77a, a candidate model with a lower score value (higher evaluation) is displayed at a higher rank. Further, in the quality-related factor information 77a, a list of theoretical models whose degree of similarity is equal to or greater than a predetermined value, for example, is shown in association with each candidate model. In the list of theoretical models, the higher the similarity, the higher the theoretical model.

The quality-related factor information 77a indicates the meaning of the theoretical model, the meaning of the quality-related factor, the candidate model, the quality-related feature, the corrected correlation coefficient, and the score value in association with each theoretical model. The meaning of the theoretical model is the physical meaning of the theoretical model, and is information obtained from the theoretical model management table 121 . The meaning of the quality-related factor is the physical meaning of the coefficient corresponding to the coefficient of the quality-related feature among the coefficients included in the theoretical model. For example, if the coefficient indicating the gain in the candidate model is the quality-related feature, the coefficient corresponding to the gain in the theoretical model (the coefficient by which the variable or function is multiplied) is the quality-related factor. Also, when the coefficient indicating the offset in the candidate model is the quality-related feature, the coefficient corresponding to the offset in the theoretical model (the coefficient added or subtracted from the variable) is the quality-related factor. The candidate model, quality-related feature, corrected correlation coefficient, and score value associated with each theoretical model are information indicating the basis for determining that the coefficient of that theoretical model is a quality-related factor.

By referring to the analysis result display screen 77, the user can recognize what kind of physical quantity is related to the quality of the product. In the example of FIG. 26, it can be understood that the exhaust resistance related to the exhaust speed affects the product quality. From this, it can be expected that the reason why the final degree of vacuum of the product is NG (defective) is caused by the exhaust resistance. Therefore, the user identifies, for example, variations in the unit piping parts that serve as exhaust resistance, and investigates the piping parts. Then, the user can prevent the occurrence of products whose final degree of vacuum does not reach the target value by taking measures to improve the variation in pipe bending shape and diameter.

Moreover, in the second embodiment, since the score value is calculated by combining the correlation coefficient and the matching coefficient, it is possible to highly accurately determine candidate models that include coefficients corresponding to factors that affect quality. can.

FIG. 27 is a diagram for explaining determination accuracy based on score values. FIG. 27 is a diagram showing an example of the analysis results of the three candidate models 78a-78c.
Candidate model 78a is represented by a six-dimensional equation. Such a high-order candidate model 78a can match the response characteristic data with high accuracy. As a result, the matching coefficient becomes a good value (small value). On the other hand, the correlation coefficient between the quality-related features of candidate model 78a and product quality is small, and the value of the modified correlation coefficient (1-absolute value of correlation coefficient) is large. Even in a candidate model 78a that accurately represents the response characteristic data, if the correlation between the included coefficients and product quality is low, the coefficients are not representative of the factors affecting quality.

Candidate model 78b matches the response characteristic data to some extent, yielding good matching coefficients. Also, the correlation coefficient between the quality-related features and the product quality of the candidate model 78b is larger than that of the candidate model 78a, and the value of the modified correlation coefficient is smaller. In other words, the candidate model 78b has good values for both the matching coefficient and the correlation coefficient.

Candidate model 78c happens to have a high correlation coefficient between quality-related features and product quality, and a low modified correlation coefficient value. If the correlation coefficient happens to be high, the value of the correlation coefficient does not represent a causal relationship between quality-related features and product quality. The candidate model 78c has a higher matching coefficient value than the other candidate models 78a and 78b.

By setting the product of the corrected correlation coefficient and the matching coefficient of each of the three candidate models 78a, 78b, and 78c as the score value, the candidate model 78b having moderately good values of the correlation coefficient and the matching coefficient is obtained. Highest score value. That is, the coefficients of the candidate model 78a, which accurately traces the response characteristic data with a higher-order expression, do not represent factors that affect quality, so the score value is bad (large). In addition, the candidate model 78c, for which the correlation coincidentally coincides, has a poor matching coefficient value (large value), thereby preventing an erroneous good score value.

In this way, by calculating the score value by combining the correlation coefficient and the matching coefficient, it is possible to appropriately extract candidate models that include coefficients representing factors that affect quality. As a result, it is possible to correctly determine the factors affecting product quality based on the relevant candidate model.

[Third Embodiment]
Next, a third embodiment will be described. A third embodiment calculates the score value by taking into account the structure of the formula, which is known in advance based on the nature of the product.

When a product contains a plurality of elements, the formula for calculating the property of the product becomes complicated, and in the second embodiment, it is difficult to determine which element among the plurality of elements causes product defects. Sometimes I don't know. Therefore, in the third embodiment, by defining the basic structure of the formula according to the product properties in advance, even if the product contains a plurality of elements, the factors affecting the product quality can be identified. allow for accurate identification.

The structure of the formula according to the nature of the product will be described below with reference to FIGS. 28 to 31. FIG.
FIG. 28 is a diagram showing a first example of the structure of formulas relating to products. The example of FIG. 28 represents the calculation formula of the tip coordinates of the hand portion of the industrial robot 81 (manipulator). The robot 81 has a plurality of joints, and the hand tip coordinates are obtained by multiplying the function f for the number of joints. If the robot 81 is a six-axis multi-joint robot, the hand tip coordinates can be obtained by multiplying the function f six times. That is, the coordinates of the tip of the hand are represented by the formula of "fxfxfxfxfxf" as a basic structure.

FIG. 29 is a diagram showing a second example of the structure of formulas relating to products. The example of FIG. 29 represents a calculation formula for the optical output of the lithium niobate (LN) modulator 82 . The basic structure of the optical output of the LN modulator 82 shown in FIG. 29 is represented by the formula “(f+f)×f”.

FIG. 30 is a diagram showing a third example of the structure of formulas relating to products. The example of FIG. 30 represents a formula for calculating the voltage V of the electric circuit 83 . Three resistors R1 to R3 are connected in parallel to the electric circuit 83, and the voltage V is represented by the formula "f+f+f" in its basic structure.

FIG. 31 is a diagram showing a fourth example of the structure of formulas relating to products. The example of FIG. 31 represents a formula for calculating the pressure loss of the fluid flowing through the pipe 84 bent like a crank. Since the pipe 84 shown in FIG. 31 has two curved portions, the pressure loss is represented by the formula of "f×f" in the basic structure.

In this way, the structure of the formula for the physical quantity to be calculated can be predicted in advance according to the properties of the product. Therefore, in the third embodiment, the data analysis unit 160 calculates the degree of similarity between the candidate model and the formula predicted for the product, and uses the degree of similarity as the structural evaluation value. Then, model evaluation section 180 calculates a score value based on the correlation coefficient, matching coefficient, and structure evaluation value.

The third embodiment will be described in detail below.
FIG. 32 is a flow chart showing an example of the quality influence cause identifying process procedure according to the third embodiment. The processing shown in FIG. 32 will be described below along with the step numbers.

[Step S201] The candidate model constructing unit 150 receives input specifying elements used in constructing a candidate model. For example, the user provides inputs specifying what the variables of the candidate model should be, what operators to use, and what functions to use. The user can also specify one of the mathematical expression candidate element lists in the mathematical expression candidate element storage unit 110 instead of inputting the designation of individual elements. When a mathematical expression candidate element list is specified, the candidate model construction unit 150 uses the operators, functions, and variables indicated in the designated mathematical expression candidate element list as elements to be used for constructing the candidate model.

Also, the user inputs the basic structure of the calculation formula according to the target product. For example, if the product is a six-axis robot 81, the user inputs "fxfxfxfxfxf" as the basic structure.

The user also inputs a weight for each index (matching coefficient, correlation coefficient, structural evaluation value) that serves as a basis for score value calculation. The user increases the weight value of the more important index.

The user also inputs termination conditions for candidate model building. For example, the user inputs a score value threshold as an end condition. The user may input a structure evaluation threshold, a matching coefficient threshold, and a correlation coefficient threshold as termination conditions. In this case, for example, when the candidate model construction unit 150 detects a candidate model having a structure evaluation value (similarity) equal to or less than the threshold, a matching coefficient equal to or less than the threshold, and a correlation coefficient equal to or greater than the threshold, the candidate model construction unit 150 ends construction of the candidate model. do.

When a score value threshold is input, the candidate model construction unit 150 holds the input threshold as an end condition. Note that, if the threshold value as the termination condition is not input, the candidate model construction unit 150 uses, for example, a preset threshold value as the termination condition.

[Step S202] The candidate model construction unit 150 constructs a candidate model by combining mathematical expression candidate elements by GP. Note that in the third embodiment, when a candidate model includes a plurality of functions, the candidate model constructing unit 150 sets gain and offset coefficients for each function. The candidate model constructing unit 150 also sets coefficients by which variables are multiplied. For example, the candidate model construction unit 150 constructs a candidate model of "acos(bt+c)+[dsin(et+f)+g sin(et+f)]×fhsin(et+f)". This candidate model contains the coefficients "a, b, c, d, e, f".

[Step S203] The data analysis unit 160 calculates values of coefficients included in the constructed candidate model for each response characteristic data acquired from the product to be analyzed. As a result, the formula for the candidate model is determined.

[Step S204] The data analysis unit 160 calculates the structural evaluation value of the constructed candidate model. For example, the data analysis unit 160 calculates the degree of similarity between the constructed candidate model and the formula representing the basic structure of the product, and uses the degree of similarity as the structural evaluation value.

At this time, the data analysis unit 160 may compare the calculated structural evaluation value with a threshold for the structural evaluation value. In that case, if the structure evaluation value is less than the threshold, the data analysis unit 160 advances the process to step S205, and if the structure evaluation value is greater than or equal to the threshold, skips the processes of steps S205 to S207 and continues the process. Proceed to step S208.

[Step S205] The data analysis unit 160 calculates a matching coefficient for each product for the constructed candidate model. For example, the smaller the residual between the response characteristic data of the product and the curve of the candidate model for which the coefficient is set, the smaller the matching coefficient.

At this time, the data analysis unit 160 may compare the calculated matching coefficient with a matching coefficient threshold. In that case, data analysis unit 160 advances the process to step S206 if the matching coefficient is less than the threshold, and skips steps S206 and S207 if the matching coefficient is greater than or equal to the threshold, and proceeds to step S208. proceed to

[Step S206] The data analysis unit 160 performs a correlation analysis between each coefficient in the candidate model and the product quality. Correlation analysis calculates a correlation coefficient for each coefficient of each constructed candidate model.

At this time, the data analysis unit 160 may compare the calculated correlation coefficient with a threshold value of the correlation coefficient. In that case, if the correlation coefficient is greater than the threshold, data analysis unit 160 advances the process to step S207, and if the correlation coefficient is equal to or less than the threshold, skips step S207 and advances the process to step S208. .

[Step S207] The model evaluation unit 180 calculates the score value of the candidate model based on the correlation coefficient for each coefficient in the candidate model, the matching coefficient, and the structural evaluation value.
[Step S208] The model evaluation unit 180 determines whether or not the termination condition for constructing the candidate model is satisfied. For example, if there is at least one candidate model whose structural evaluation value is less than the threshold, the matching coefficient is less than the threshold, the correlation coefficient is greater than the threshold, and the score value is less than the threshold, the model evaluation unit 180 sets the end condition to determine that it satisfies If the termination condition is satisfied, the model evaluation unit 180 advances the process to step S209. If the termination condition is not satisfied, the model evaluation unit 180 advances the process to step S202. If the termination condition is not satisfied, the model evaluation unit 180 transmits, for example, two candidate models with the highest score values among the candidate models of the latest generation to the candidate model construction unit 150 .

[Step S209] The model evaluation unit 180 compares a predetermined number of candidate models with the smallest score values with the theoretical model. The model evaluation unit 180 calculates, for example, the structural similarity between the candidate model and the theoretical model. Then, the model evaluation unit 180 determines the meaning of the coefficients of the candidate model based on the meaning of the coefficients of the theoretical model similar to the candidate model.

[Step S210] The model evaluation unit 180 outputs the result of identifying the cause of quality influence. For example, the model evaluation unit 180 displays on the monitor 21 the meanings of the coefficients of a predetermined number of candidate models in ascending order of score value as factors affecting product quality.

The process of identifying the cause of quality influence is performed in such a procedure. As described above, the third embodiment is significantly different from the second embodiment in that the score value is calculated using the structural evaluation value.
FIG. 33 is a diagram illustrating a calculation example of a structure evaluation value; The data analysis unit 160 simplifies the candidate model 91 to generate the structure of the calculation formula of the candidate model 91 (candidate model structure 91a). For example, the data analysis unit 160 simplifies the candidate model by the character string replacement process shown in FIG. 22, for example.

The data analysis unit 160 then calculates a structure evaluation value based on the degree of similarity between the basic structure 90 and the candidate model structure 91a. For example, the data analysis unit 160 calculates the minimum number of edits (Levenshtein distance) for converting the candidate model structure 91a into the basic structure 90 using the Levenshtein distance method. The data analysis unit 160 uses, for example, a value obtained by dividing the minimum number of edits by the number of characters in the basic structure as the structure evaluation value.

The data analysis unit 160 determines that the candidate model 91 conforms to the basic structure 90, for example, when the calculated structure evaluation value is less than the threshold value of the structure evaluation value. Further, the data analysis unit 160 determines that the candidate model 91 is incompatible with the basic structure 90 when the calculated structure evaluation value is equal to or greater than the threshold value of the structure evaluation value. In the case of incompatibility, the data analysis unit 160 sets a structural incompatibility flag in the record of the candidate model 91 in the evaluation result management table 181 (see FIG. 19), for example. When the structure of the candidate model 91 is unsuitable, the data analysis unit 160 omits the calculation of the matching coefficient of the candidate model 91 and the correlation analysis process, thereby improving the efficiency of the process.

In the third embodiment, the model evaluation unit 180 calculates the score value of the candidate model based on the order (ranking) for each index (structural evaluation value, matching coefficient, correlation coefficient) among the candidate models. . The candidate models are ranked for each index and set in the ranking management table.

FIG. 34 is a diagram showing an example of a ranking management table. In the ranking management table 92, rankings of structure evaluation values, matching coefficients, and correlation coefficients are set in association with individual numbers of candidate models.

The ranking of structural evaluation values is the order of each candidate model when a plurality of candidate models are sorted in ascending order of structural evaluation value. Therefore, the candidate model with the smallest structural evaluation value ranks first in the structural evaluation value ranking.

The matching coefficient ranking is the order of each candidate model when a plurality of candidate models are sorted in ascending order by matching coefficient. Therefore, the candidate model with the smallest matching coefficient is ranked first in terms of matching coefficient.

The correlation coefficient ranking is the order of each candidate model when multiple candidate models are sorted in descending order of correlation coefficient. Therefore, the candidate model with the largest correlation coefficient is ranked first in terms of correlation coefficient.

The model evaluation unit 180 weights the ranking of each index and calculates a score value. For example, the model evaluation unit 180 divides each index by the weight of the index for each candidate model, and sets the sum of the division results as the score value of each candidate model. The score value is represented by the following formula.
Score value = (structural evaluation value ranking/structural evaluation value weight Wf) + (matching coefficient ranking/matching coefficient weight Wr) + (correlation coefficient ranking/correlation coefficient weight Wc)
The model evaluation unit 180 sets the calculated score value in the ranking management table 92 . The model evaluation unit 180 stores the created ranking management table 92 in the memory 102 .

The model evaluation unit 180 compares the score values of the constructed candidate models and extracts the candidate model with the highest score value as the optimum model. The model evaluation unit 180 then compares the candidate model extracted as the optimum model with the theoretical model to determine the meaning of the coefficients that affect quality.

FIG. 35 is a diagram illustrating an example of matching between candidate models and theoretical models. In the example of FIG. 35, the meaning of the theoretical model, the coefficients included in the theoretical model, and the meaning of each coefficient are set in association with the theoretical model in the theoretical model management table 121a.

The model evaluation unit 180 simplifies, for example, the candidate model 91 extracted as the optimum model and the theoretical model, and calculates the degree of similarity using the Levenshtein distance method. Then, the theoretical models are sorted by similarity (minimum number of edits). Next, the model evaluation unit 180 identifies coefficients corresponding to coefficients indicating quality-related features in the candidate model among the coefficients in the theoretical model with high similarity. Then, the model evaluation unit 180 displays the meaning of the specified coefficient on the monitor as the analysis result.

FIG. 36 is a diagram showing an example of an analysis result display screen for quality-related factors. On the analysis result display screen 93, the equations of the theoretical model are displayed in descending order of rank (in ascending order of score value). Each theoretical model is associated with its meaning and the coefficients it contains. Associated with each coefficient is its meaning, matching coefficient, correlation coefficient, and structural evaluation value. Information about coefficients that represent quality-related features among the coefficients contained in the theoretical model are highlighted.

In this way, by setting the basic structure according to the properties of the product in advance, it is possible to extract candidate models that are suitable for the basic structure.
A plurality of basic structures may be defined for one type of product. For example, the physical properties of a product may be complex, and there may be multiple basic structures that may represent the properties, making it difficult to limit to one basic structure. In that case, the model evaluation unit 180 calculates the score value of each candidate model for each basic structure. Then, the model evaluation unit 180 displays similar theoretical models and the meanings of the coefficients in the theoretical models in descending order of the score value calculated for each basic structure.

FIG. 37 is a diagram showing an example of an analysis result display screen of quality-related factors when there are a plurality of basic structures. The example of FIG. 37 is a case of calculating the score value for each candidate model based on two basic structures 90a and 90b. The model evaluation unit 180 sorts the records corresponding to the pairs of the theoretical model and the basic structure similar to the candidate model in ascending order of the score values, and displays them on the analysis result display screen 94 .

On the analysis result display screen 94, the basic structure matching portion is displayed in association with the theoretical model. The base structure matching section displays the base structure from which the score value was calculated, and highlights the coefficients identified as quality-relevant features within that base structure.

In this way, the optimum model can be determined by considering the structure of the product, and the factors affecting the quality of the product can be accurately specified.
[Other embodiments]
In the second and third embodiments, candidate models are constructed by GP, but candidate models may be constructed by other methods. As a termination condition for candidate model construction, for example, the number of constructed candidate models exceeding the maximum amount, or the generation of candidate models constructed by GP reaching a predetermined generation may be used.

In addition, in the second embodiment, the product of the matching coefficient and the corrected correlation coefficient is used as the score value. A score value may be calculated based on the ranking with

Further, methods other than the Levenshtein distance method may be used for calculating the degree of similarity between the candidate model and the theoretical model and the degree of similarity between the candidate model and the basic structure.
Although the embodiment has been exemplified above, the configuration of each part shown in the embodiment can be replaced with another one having the same function. Also, any other components or steps may be added. Furthermore, any two or more configurations (features) of the above-described embodiments may be combined.

REFERENCE SIGNS LIST 10 information processing device 11 storage unit 11a measurement data 12b quality data 12 processing unit

Claims (11)

a storage unit for storing measurement data indicating temporal changes in measured values obtained by measuring physical quantities during work on each of a plurality of products of the same type, and quality data including quality values representing the quality of each of the plurality of products;
generating a plurality of candidate formulas that include coefficients whose values are undetermined and that express temporal changes in the physical quantity; subjecting each of the plurality of generated candidate formulas to evaluation; A coefficient value is determined for each product, and a matching coefficient indicating the degree of conformity of the candidate formula to be evaluated with respect to the measured value is calculated based on the coefficient value of the candidate formula to be evaluated for each product. A score value of the candidate formula to be evaluated is calculated based on the matching coefficient and the correlation coefficient of the candidate formula to be evaluated. is calculated, and based on the score value of each of the plurality of candidate formulas, a processing unit that identifies a quality-related formula including a coefficient related to the quality of the plurality of products from among the plurality of candidate formulas;
Information processing device having The processing unit calculates the residual between the regression equation obtained by setting the coefficient value for each product to the candidate equation to be evaluated and the measured value for each product, and calculates the average of the absolute values of the residuals for the matching. Let the coefficient be
The information processing apparatus according to claim 1. The processing unit generates the plurality of candidate formulas by genetic programming,
The information processing apparatus according to claim 1 or 2. The processing unit further identifies a similar theoretical formula similar to the quality-related formula from among the plurality of theoretical formulas representing the theoretical properties of the plurality of products, output a meaningful meaning,
4. The information processing apparatus according to any one of claims 1 to 3. The processing unit sets a product of the matching coefficient and a value corresponding to the correlation coefficient for the candidate expression to be evaluated as the score value of the candidate expression to be evaluated.
5. The information processing apparatus according to any one of claims 1 to 4. When the candidate expression to be evaluated includes a plurality of coefficients, the processing unit performs a value corresponding to the correlation coefficient having a larger absolute value among the correlation coefficients of the plurality of coefficients, and The score value of the candidate expression to be evaluated is the product of the matching coefficient and
6. The information processing apparatus according to claim 5. The processing unit multiplies or divides a weight corresponding to each of the matching coefficient and the correlation coefficient of the candidate expression to be evaluated, and calculates the sum of the weight multiplication or division results as the candidate expression to be evaluated. Let the score value be
5. The information processing apparatus according to any one of claims 1 to 4. The processing unit determines ranks of the matching coefficients and the correlation coefficients among the plurality of candidate expressions, based on the ranks of the matching coefficients and the correlation coefficients of the candidate expressions to be evaluated. to calculate the score value of the candidate expression to be evaluated;
The information processing apparatus according to any one of claims 1 to 7. The processing unit calculates a structural evaluation value of the candidate formula to be evaluated based on the degree of similarity between the basic structure of the formula for calculating the physical quantity based on the characteristics of the plurality of products and the candidate formula to be evaluated. calculating the score value of the candidate formula to be evaluated based on the matching coefficient, the correlation coefficient, and the structure evaluation value of the candidate formula to be evaluated;
The information processing apparatus according to any one of claims 1 to 8. the computer
storing, in a storage unit, measurement data indicating temporal changes in measured values obtained by measuring physical quantities during work on each of a plurality of products of the same type, and quality data including quality values representing the quality of each of the plurality of products;
generating a plurality of candidate formulas including coefficients whose values are undetermined and representing changes in the physical quantity over time;
Each of the plurality of generated candidate formulas is evaluated, a coefficient value of the coefficient of the candidate formula to be evaluated is determined for each product based on the measured value, and the coefficient value of the candidate formula to be evaluated is determined for each product. calculating a matching coefficient indicating the degree of conformity of the candidate formula to be evaluated with respect to the measured value; calculating a correlation coefficient between the coefficient value of the candidate formula to be evaluated for each product and the quality value; calculating a score value of the candidate expression to be evaluated based on the matching coefficient and the correlation coefficient of the candidate expression to be evaluated;
Based on the score value of each of the plurality of candidate formulas, identifying a quality-related formula including coefficients related to the quality of the plurality of products from among the plurality of candidate formulas;
How to generate a quality-associated expression. to the computer,
storing, in a storage unit, measurement data indicating temporal changes in measured values obtained by measuring physical quantities during work on each of a plurality of products of the same type, and quality data including quality values representing the quality of each of the plurality of products;
generating a plurality of candidate formulas including coefficients whose values are undetermined and representing changes in the physical quantity over time;
Each of the plurality of generated candidate formulas is evaluated, a coefficient value of the coefficient of the candidate formula to be evaluated is determined for each product based on the measured value, and the coefficient value of the candidate formula to be evaluated is determined for each product. calculating a matching coefficient indicating the degree of conformity of the candidate formula to be evaluated with respect to the measured value; calculating a correlation coefficient between the coefficient value of the candidate formula to be evaluated for each product and the quality value; calculating a score value of the candidate expression to be evaluated based on the matching coefficient and the correlation coefficient of the candidate expression to be evaluated;
Based on the score value of each of the plurality of candidate formulas, identifying a quality-related formula including coefficients related to the quality of the plurality of products from among the plurality of candidate formulas;
A quality-associated expression generator that runs the process.

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